Graph modulations for massive MIMO systems

A new graph modulation scheme is proposed for massive multiple-input multiple-output (MIMO) systems with a large number of transmit antennas. Each data symbol is transmitted in the form of multiple weighted replicas. The replicas from different symbols are multiplexed onto a two-dimensional (2D) space-time grid, which is formed by multiple transmit antennas in the space domain and different transmission instants in the time domain. Multiplexing repeated symbols onto a 2D space-time grid achieves performance gains in terms of both diversity gain and high degree-of-freedom of the received signals. In addition, it enables a bipartite graph representation of the system, with one set of nodes being the transmitted symbols and the other set containing the received space-time samples. A modified message passing algorithm is proposed to iteratively detect the transmitted symbols by exploiting the structure of the bipartite graph. The proposed graph modulation scheme can flexibly adjust the tradeoff among energy efficiency, spectral efficiency, space diversity, and detection complexity by choosing different design parameters based on application requirements. Simulation results demonstrate that the proposed approach can achieve significant performance gains over the conventional spatial multiplexing scheme used in MIMO systems.